dirichlet_hho.cc
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#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "dirichlet_homogeneous.h"
#include "diffusion_isotropic.h"
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
string Pkd = (argc > 2) ? argv[2] : "P1d",
Pld = (argc > 3) ? argv[3] : Pkd;
Float beta = (argc > 4) ? atof(argv[4]) : 1;
space Xh (omega, Pld),
Mh (omega["sides"], Pkd);
Mh.block("boundary");
size_t k = Xh.degree(), l = Mh.degree(), d = omega.dimension();
check_macro(l == k-1 || l == k || l == k+1,
"invalid (k,l) = ("<<k<<","<<l<<")");
space Xhs(omega, "P"+itos(k+1)+"d"),
Zh (omega, "P0"),
Mht(omega, "trace(P"+itos(k)+"d)");
space Yh = Xh*Xhs*Xh*Mht*Zh;
trial x(Yh), lambda(Mh);
test y(Yh), mu(Mh);
auto u = x[0], us = x[1], ut = x[2], deltat = x[3], zeta = x[4];
auto v = y[0], vs = y[1], vt = y[2], gammat = y[3], xi = y[4];
integrate_option iopt;
iopt.invert = true;
form inv_a = integrate(dot(grad_h(us),a(d)*grad_h(vs))
+ dot(grad_h(us)-grad_h(u),a(d)*(grad_h(vs)-grad_h(v)))
+ (us-u)*xi + (vs-v)*zeta + (ut-us)*(vt-vs)
+ on_local_sides(beta/h_local()*deltat*gammat
+ u*dot(a(d)*grad_h(vs),normal())
+ v*dot(a(d)*grad_h(us),normal())
+ (deltat - us + ut)*(gammat - vs + vt)), iopt);
form b = integrate(omega,on_local_sides(-mu*dot(a(d)*grad_h(us),normal())));
// TODO: remove omega, autodetect it ?
field lh = integrate (f(d)*v);
// TODO: f -> -f ? check the FV...
field lambda_h(Mh,0);
form s = b*inv_a*trans(b);
field rh = b*(inv_a*lh);
problem p (s);
p.solve (rh, lambda_h);
field xh = inv_a*(lh - b.trans_mult(lambda_h));
dout << catchmark("beta") << beta << endl
<< catchmark("u") << xh[0]
<< catchmark("us") << xh[1]
<< catchmark("ut") << xh[2]
<< catchmark("delta") << xh[3]
<< catchmark("zeta") << xh[4]
<< catchmark("lambda") << lambda_h;
}
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
Float
see the Float page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
problem
see the problem page for the full documentation
rheolef::catchmark
see the catchmark page for the full documentation
Definition: catchmark.h:67
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
rheolef::integrate_option
see the integrate_option page for the full documentation
Definition: integrate_option.h:125
rheolef::integrate_option::invert
bool invert
Definition: integrate_option.h:168
rheolef::std
Definition: vec_expr_v2.h:402
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
diffusion_isotropic.h
Tensor diffusion – isotropic case.
main
int main(int argc, char **argv)
Definition: dirichlet_hho.cc:30
dirichlet_homogeneous.h
The Poisson problem with homogeneous Dirichlet boundary conditions – right-hand-side and boundary con...
mkgeo_ball.b
int b
Definition: mkgeo_ball.sh:152
mkgeo_ball.f
int f
Definition: mkgeo_ball.sh:221
mkgeo_ball.d
int d
Definition: mkgeo_ball.sh:154
mkgeo_ball.a
int a
Definition: mkgeo_ball.sh:151
mkgeo_contraction.mu
mu
Definition: mkgeo_contraction.sh:193
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
rheolef::h_local
details::field_expr_v2_nonlinear_terminal_function< details::h_local_pseudo_function< Float > > h_local()
h_local: see the expression page for the full documentation
Definition: field_expr_terminal.h:527
rheolef::trans
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition: csr.h:455
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
dot(x,y): see the expression page for the full documentation
Definition: vec_expr_v2.h:415
rheolef::grad_h
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:949
rheolef::on_local_sides
std::enable_if< details::is_field_expr_v2_variational_arg< Expr >::value,details::field_expr_quadrature_on_sides< Expr > >::type on_local_sides(const Expr &expr)
on_local_sides(expr): see the expression page for the full documentation
Definition: field_expr_quadrature.h:321
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
rheolef::itos
std::string itos(std::string::size_type i)
itos: see the rheostream page for the full documentation
rheolef::normal
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition: field_expr_terminal.h:439
rk::beta
Float beta[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:60
rheolef.h
rheolef - reference manual
lambda
Definition: yield_slip_circle.h:34
p
Definition: sphere.icc:25
u
Definition: leveque.h:25